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where
i
x is the mean over all pixels of the i-th picture. In addition, a matrix for the correlation between
any two of these images can be calculated according to the following:
),(),(
),(
),(
jjCiiC
jiC
jir =
2) To calculate eigenvalue vector λ of the co-variance matrix C and to compute eigen-matrix B so as to
constitute the transforming matrix T. Solve ⏐λI – C⏐ = 0, where I is a unit matrix, for λ to obtain all
eigenvaluesλ
i
(i = 1, 2, …, M), which are then put in decreasing order; then solve the equation
()
0=−
i
bCI
G
λ
to obtain eigenvector
i
b
= [b
1i,
b
2i
,…b
Mi
]
T
, which are used to constitute the
characteristic matrix B, i.e., B = [
1
b
,
2
b
,…
M
b
], and further the transforming matrix T = B
T
.
3) Let Y = B
T
X = TX, resulting in a new matrix Y, in which the vector on the i-th row y
i
=[y
i1
,y
i2
,…y
iN
] is
the i-th principal component from the transform and is thus the i-th principal feature of the M images.
The i-th principal feature contains a certain percentage of information of the M images, and the
percentage is defined as
∑
=
=
M
i
iii
p
1
*100
λλ
Since the eignevalues have been arranged in descending order, the first principal feature y
1
=[y
11
,y
12
,…y
1N
]
has the largest volume of information of the M images in percentage while the M-th principal feature
y
M
=[y
M1
,y
M2
,…y
MN
] contains the least.
3. Image Features From The FY-1 Satellite
The 10-waveband scanning radiometer onboard the FY-1C/D satellite has spectral characteristics as
shown in Table 1, indicating that the visible channels 1, 2 (including near IR waveband), 7, 8 and 9 obtain
the information on the intensity of solar beams reflected mainly by bodies on the surface and in the
atmosphere; the IR channels 4 and 5 the information about the temperature of earth’s surface and cloud
top. The albedoes or radiation temperatures vary from body to body, leading to the differences in
brightness on the image for a researcher or forecaster to identify a particular target. In general, a thick
multi-layer cloud system is marked by high albedo or cold cloud top, exhibiting high brightness and, in
contrast, land and water surfaces are warmer or lower albedo, making for less brightness – all these
constitute the dominant peculiarity of a cloud map sent from the 10 channels.
Table 1. Band position of the FY-1C/D 10-channel radiometer and its main applications
表 1 FY-1C/D 十通道频带范围及各通道主要用途
---------------------------------------------------------------------------------------------------------------------
channel wavelength (µm) targets and applications
---------------------------------------------------------------------------------------------------------------------
1 0.58~0.68 (visible) cloud, ice/snow cover, and vegetation during
daytime hours
2 0.84~0.89 (visible~near IR) cloud cover, vegetation, and water by day
3 3.55~3.95 (shortwave IR) heat source, (e.g., for forest fire monitoring) and
nighttime cloud cover